To quantify coherence, Baumgratz et al. established a framework by referring to the method of quantifying entanglement [1]}.
The quantum coherence of a quantum state is defined as the minimum distance between the quantum state and an incoherent state in the Hilbert space [1]}. In addition to relative entropy and \(l_{1}\) -norm [1]}, it has been shown that quantum coherence can also be quantified by Fisher information [4]}, skew information entropy [5]}, Tsallis relative \(\alpha \)  entropy [6]}, robustness [7]}, and so on.
The frozen [8]}, distillation [9]}, catalytic [10]}, and erasure [11]} of quantum coherence and the relationships between quantum coherence and complementarity relation[12]}, uncertainty relation[13]}, quantum entanglement or other types of quantum correlation [14]}, [15]} have also been investigated.
With the rapid development in quantum coherence theory, the experimental demonstration related to quantum coherence is in progress [16]}, [17]}, [18]}, [19]}, [20]}, [21]}.
Gaussian states, such as the squeezed state and the Einstein-Podolsky-Rosen (EPR) entangled state, play essential roles in continuous variable (CV) quantum information [22]}, [23]}, [24]}, where Gaussian states are generated deterministically and information is encoded in the position or momentum quadrature of photonic harmonic oscillators. For example, Gaussian states has been applied in quantum computation [25]}, [26]}, quantum key distribution [27]}, [28]}, [29]}, quantum teleportation [30]}, [31]}, quantum entanglement swapping [32]}, [33]}, [34]}, quantum dense coding [35]}, [36]}, and verification of the error-disturbance uncertainty relation [37]}, [38]}. Recently, it has been shown that quantum coherence with infinite-dimensional systems can be quantified by relative entropy [39]}. Then, the investigations of Gaussian quantum coherence attracted lots of attention [40]}, [41]}, [42]}.
